Methods and apparatus for bi-stable actuation of displays

ABSTRACT

The invention relates to mechanically bi-stable shutter assemblies for use in display apparatus to form images.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation in part of U.S. patent applicationSer. No. 11/218690, filed Sep. 2, 2005. This application claims priorityto, and the benefit of, U.S. Provisional Patent Application No.60/676,053, entitled “MEMS Based Optical Display” and filed on Apr. 29,2005; and U.S. Provisional Patent Application No. 60/655,827, entitledMEMS Based Optical Display Modules” and filed on Feb. 23, 2005. Allthree applications are incorporated herein by reference.

FIELD OF THE INVENTION

In general, the invention relates to the field of video displays, inparticular, the invention relates to mechanically actuated displayapparatus.

BACKGROUND OF THE INVENTION

Displays built from mechanical light modulators are an attractivealternative to displays based on liquid crystal technology. Mechanicallight modulators are fast enough to display video content with goodviewing angles and with a wide range of color and grey scale. Mechanicallight modulators have been successful in projection displayapplications. Backlit displays using mechanical light modulators havenot yet demonstrated sufficiently attractive combinations of brightnessand low power. There is a need in the art for fast, bright, low-poweredmechanically actuated displays. Specifically there is a need formechanically actuated displays that include bi-stable mechanisms andthat can be driven at low voltages for reduced power consumption.

SUMMARY OF THE INVENTION

In one aspect, the invention relates to displays built from mechanicalactuators which incorporate two compliant electrodes. The actuators maybe controlled by passive or active matrix arrays coupling controllablevoltage sources to the voltage inputs of the mechanical actuators.

The compliant electrodes in each actuator are positioned proximate toone another, such that in response to the application of a voltageacross the electrodes, the electrodes are drawn together. The electrodesmay be drawn together directly or progressively. At least one of theelectrodes couples to a modulator which contributes to the formation ofan image. According to one feature of the invention, at least a majorityof the lengths of the electrodes are compliant. The electrodes may beabout 0.5 μm to about 5 μm wide. In one implementation, the height ofthe electrodes is at least about 1.4 times the width of the electrodes.The electrodes may also be coated, at least in part with an insulator,preferably having a dielectric constant of about 1.5 or greater.

The modulator may be, for example, a shutter, a deformable mirror, acolor filter, or a set of three color filters. Shutters movesubstantially in a plane parallel to a surface over which they aresupported. The surface may have one or more apertures allowing thepassage of light through the surface. The apertures may be patternedthrough a reflective film disposed on a substantially transparent glassor plastic substrate. If the surface has more than one aperture, theshutter includes a corresponding number of shutter apertures. By movingthe shutter, the display apparatus can selectively interact with lightin an optical path passing through the apertures in the surface byeither blocking reflecting, absorbing, polarizing, diffracting and/orfiltering the light. In various embodiments, the shutter may also becoated with a reflective or light absorbing film.

In one embodiment, one end of each electrode is anchored to the surfaceand the other end is free to move. In this embodiment, the modulatorcouples to the free end of one of the electrodes. The width of theelectrode may be constant along its length, or it may vary. For example,it may become thinner closer to the modulator. Alternatively, theelectrode may have thinner sections and thicker sections at multiplelocations along the length of the electrode. The varying thicknessesprovide for varying electrode stiffnesses. The embodiment may include anoptional feature of including a third compliant electrode. The compliantelectrodes not coupled to the modulator act separately as open and closedrive electrodes. One or both of the drive electrodes may be curved inits natural, deactivated state. In some implementations, the driveelectrodes have a first or second order curve. In other implementations,the drive electrodes have a greater than second order curve.

In another embodiment of the shutter assembly, a shutter couples to apair of actuators at about the linear center of one side of themodulator. The actuators each include two compliant electrodes. A firstcompliant electrode of each actuator couples to the shutter with aspring. The first compliant electrode may also couple to the anchor witha spring. The other ends of the compliant electrodes couple to anchors,thereby connecting the shutter to two locations on a substrate. Theelectrodes serve as mechanical supports providing supportive connectionsfrom locations on the shutter to the substrate. A separate elasticmember, such as a return spring, may couple to an opposite side of theshutter, providing an additional supportive connection for the shutter.Alternatively, a second pair of actuators may couple to the oppositeside of the shutter instead of the return spring. The multiplesupportive connections help reduce rotation or other movement of theshutter out of its intended plane of motion.

In a second aspect of the invention, the display apparatus includes amechanically bi-stable shutter assembly to form an image. A mechanicallybi-stable shutter assembly includes a shutter, a voltage input forreceiving an actuation potential and an actuator that moves a shutterover a substrate between two mechanically stable positions. In oneembodiment, the work needed to move the shutter from its firstmechanically stable position to its second mechanically stable positionis greater than the work need to return the shutter to its firstmechanically stable position. In another embodiment, the amount of workneeded to move the shutter from its first mechanically stable positionto its second mechanically stable position is substantially equal to thework needed to return the shutter to its first mechanically stableposition.

According to one feature of the invention, the mechanically stablepositions of the shutter are provided by the state, including theposition or shape, of a mechanically compliant member. In oneembodiment, the mechanically compliant member is part of the actuator.In other embodiments, the mechanically compliant member is outside ofthe actuator. The mechanically compliant member has a first mechanicallystable state in a first of the shutter's mechanically stable positionsand a second mechanically stable state in the second of the shutter'smechanically stable position. Moving the shutter from the firstmechanically stable position to the second mechanically stable positionrequires the deformation of the compliant member.

For example, the compliant member may be a curved compliant beam. Whenthe shutter is in the first stable position, the beam has a firstcurvature. The beam has a second curvature when the shutter is in thesecond position. The curvature may be generally “s” shaped or it mayform a cosine shaped bow. In the first shutter position, the beam maybow in one direction. In transitioning to the second shutter position,the beam is deformed such that bows in an opposite direction.

Alternatively, the compliant beam may be straight while the shutter isin one of its mechanically stable position. The compliant beam forms afirst angle with the shutter in the first mechanically stable shutterposition. In the second position, the compliant beam forms a differentangle with the shutter.

The shutter assembly may also include a second compliant member. Thefirst and second compliant members, in one embodiment, serve aselectrodes in a dual compliant beam electrode actuator. One or bothbeams may have two mechanically stable states. Upon application of avoltage across the compliant members, one of the compliant membersdeforms from one position to a second position. The voltage may resultfrom an actuation potential being applied to one of the compliantmembers from one or more anchors coupled to one or both ends of thecompliant member. For example, in the first position, the firstcompliant electrodes bows away from the second compliant electrode. Inthe second position, the first compliant electrode bows towards thesecond compliant electrode, having a substantially similar bow as thesecond compliant electrode. In other implementations, the first andsecond compliant beams form part of an thermoelectric actuator coupledto the shutter for moving it between the first and second stablepositions. Regardless of the type of actuator moving the shutter, tomove the shutter, a force must be applied to either the first or secondcompliant member.

In some embodiments, the first and second compliant member shapes arethemselves mechanically stable.

The shutter assembly, in one implementation, includes a second actuatorcoupled to the shutter. The two actuators couple to the shutter indifferent locations on the shutter. According to one implementation, theactuators couple to opposite sides of the shutter, at about the middleof the sides. Compliant members in the actuators provide supportiveconnections for the shutter from two shutter locations to two substratelocations. According to another optional feature, at least one of thecompliant members coupled to the shutter couples to two anchors, one oneither end the compliant member.

In still other embodiments, the compliant members are incorporated intoa stabilizer which provides the mechanical stability for themechanically stable shutter positions. The compliant members in astabilizer may be connected to one another. In such an embodiment, thestabilizer may provide for a third mechanically stable shutter position.The shutter is driven into the third mechanically stable shutterposition in response to an application of a second actuation voltage tothe voltage input. Alternatively, the compliant beams may form astabilizer by coupling to anchors on either side of the shutter to sidesof the shutter. The compliant members may include compliant or rigidbeams. If the compliant members include rigid beams, the compliantmembers include additional compliant joints between the rigid beams toprovide a degree of compliance.

Additional features of the various display apparatus include theincorporation of a working fluid among the compliant members. Theworking fluid preferably has a dielectric constant of at least about1.5. The display apparatus may also include a backlight for illuminatingthe image.

In another aspect, the invention relates to a method of manufacturing adisplay apparatus. The method includes patterning a first surface toform a modulator for selectively interacting with light in an opticalpath. An actuator is then fabricated in the first surface connecting themodulator and an anchor. The anchor and the actuator serve as a firstmechanical support, physically supporting the modulator over a secondsurface. The actuator is configured to drive the shutter in a planesubstantially parallel to the second surface. The method furtherincludes fabricating a second mechanical support into first surfaceconnecting the modulator and a second anchor. The second mechanicalsupport physically supports the modulator over the second surface. Thefirst anchor and the second anchor are connected to two distinctlocations on the second surface.

In another aspect, the invention relates to a method of forming animage. The method includes selectively applying an actuation potentialto a voltage input of a shutter assembly. A shutter is moved in a planesubstantially parallel to a surface, in response to the application ofthe actuation voltage. The shutter is moved from a first mechanicallystable position to a second mechanically stable position, therebypermitting light to contribute to the formation of an image.

In still a further aspect, the invention relates to a method of formingan image on a display. The method includes selecting a light modulatorand providing an actuator. The actuator includes two mechanicallycompliant electrodes positioned proximate to one another, at least oneof which couples to a shutter. The actuator is activated by generating avoltage between the two mechanically compliant electrodes. As a result,the compliant electrodes deform as they are drawn closer together. Inaddition, the activation of the actuator results in movement of theshutter into or out of an optical path to affect the illumination of apixel in the image.

BRIEF DESCRIPTION OF THE DRAWINGS

The system and methods may be better understood from the followingillustrative description with reference to the following drawings inwhich:

FIG. 1 is conceptual isometric view of a display apparatus, according toan illustrative embodiment of the invention;

FIGS. 2A-2B are top views of dual compliant beam electrodeactuator-based shutter assemblies for use in a display apparatus,according to an illustrative embodiment of the invention;

FIG. 3A is a diagram illustrating various compliant electrode shapessuitable for inclusion in dual compliant electrode actuator-basedshutter assemblies;

FIG. 3B is a diagram illustrating the incremental energy needed to movedual compliant electrode actuator-based shutter assemblies having theshapes illustrated in FIG. 3A;

FIGS. 3C-3F are top views of the compliant beam electrode actuator-basedshutter assembly of FIG. 2A in various stages of actuation.

FIGS. 4A and 4B are cross section views of a dual compliant electrodeactuator-based mirror-based light modulator in an active and an inactivestate, according to an illustrative embodiment of the invention;

FIG. 5 is a top view of a dual compliant beam electrode actuator-basedshutter assembly having a beam with thickness which varies along itslength, according to an illustrative embodiment of the invention;

FIG. 6 is an isometric view of a dual compliant beam electrodeactuator-based shutter assembly, according to an illustrative embodimentof the invention;

FIG. 7 is a top view of a dual compliant beam electrode actuator-basedshutter assembly including a return spring, according to an illustrativeembodiment of the invention;

FIG. 8 is a top view of a dual compliant beam electrode actuator-basedshutter assembly having separate open and close actuators, according toan illustrative embodiment of the invention;

FIG. 9 is a conceptual diagram of an active matrix array for controllingdual compliant electrode actuator based-light modulators, according toan illustrative embodiment of the invention;

FIG. 10 is a conceptual diagram of a second active matrix array forcontrolling dual compliant electrode actuator based-light modulators,according to an illustrative embodiment of the invention;

FIG. 11 is a cross sectional view of the dual compliant beam electrodeactuator-based shutter assembly of FIG. 8;

FIG. 12 is an energy diagram illustrating the energy characteristics ofvarious dual compliant electrode based shutter assemblies, according toan illustrative embodiment of the invention;

FIG. 13A is a top view of a bi-stable dual compliant beam electrodeactuator based-shutter assembly, according to an illustrative embodimentof the invention;

FIG. 13B shows the evolution of force versus displacement for abi-stable shutter assembly.

FIG. 14 is a top view of a second bi-stable dual compliant beamelectrode actuator based-shutter assembly, according to an illustrativeembodiment of the invention;

FIG. 15 is a top view of a tri-stable shutter assembly incorporatingdual compliant electrode actuators, according to an illustrativeembodiment of the invention;

FIGS. 16A-C are conceptual diagrams of another embodiment of a bi-stableshutter assembly, illustrating the state of the shutter assembly duringa change in shutter position, according to an illustrative embodiment ofthe invention;

FIG. 17A is a conceptual diagram of a bi-stable shutter assemblyincluding substantially rigid beams, according to an illustrativeembodiment of the invention;

FIG. 17B is a top view of a rotational bi-stable shutter assembly;

FIG. 18 is a conceptual diagram of a bi-stable shutter assemblyincorporating thermoelectric actuators, according to an illustrativeembodiment of the invention;

FIG. 19 is a conceptual diagram of a passive matrix array forcontrolling bi-stable shutter assemblies, according to an illustrativeembodiment of the invention;

FIGS. 20A and 20B are conceptual tiling diagrams for arranging shutterassemblies in a display apparatus; and

FIG. 21 is cross-sectional view of a display apparatus, according to anillustrative embodiment of the invention.

DESCRIPTION OF CERTAIN ILLUSTRATIVE EMBODIMENTS

FIG. 1A is an isometric view of a display apparatus 100, according to anillustrative embodiment of the invention. The display apparatus 100includes a plurality of light modulators, in particular, a plurality ofshutter assemblies 102 a-100 d (generally “shutter assemblies 102”)arranged in rows and columns. In general, a shutter assembly 102 has twostates, open and closed (although partial openings can be employed toimpart grey scale). Shutter assemblies 102 a and 100 d are in the openstate, allowing light to pass. Shutter assemblies 102 b and 100 c are inthe closed state, obstructing the passage of light. By selectivelysetting the states of the shutter assemblies 102 a-100 d, the displayapparatus 100 can be utilized to form an image 104 for a projection orbacklit display; if illuminated by lamp 105. In another implementationthe apparatus 100 may form an image by reflection of ambient lightoriginating from the front of the apparatus. In the display apparatus100, each shutter assembly 102 corresponds to a pixel 106 in the image104.

Each shutter assembly 102 includes a shutter 112 and an aperture 114. Toilluminate a pixel 106 in the image 104, the shutter 112 is positionedsuch that it allows light to pass, without any significant obstruction,through, the aperture 114 towards a viewer. To keep a pixel 106 unlit,the shutter 112 is positioned such that it obstructs the passage oflight through the aperture 114. The aperture 114 is defined by anopening patterned through a reflective or light-absorbing material ineach shutter assembly 102.

In alternative implementations, a display apparatus 100 includesmultiple shutter assemblies 102 for each pixel 106. For example, thedisplay apparatus 100 may include three color-specific shutterassemblies 102. By selectively opening one or more of the color-specificshutter assemblies 102 corresponding to a particular pixel 106, thedisplay apparatus 100 can generate a color pixel 106 in the image 104.In another example, the display apparatus 100 includes two or moreshutter assemblies 102 per pixel 106 to provide grayscale in an image104. In still other implementations, the display apparatus 100 mayinclude other forms of light modulators, such as micromirrors, filters,polarizers, interferometric devices, and other suitable devices, insteadof shutter assemblies 102 to modulate light to form an image.

The shutter assemblies 102 of the display apparatus 100 are formed usingstandard micromachining techniques known in the art, includinglithography; etching techniques, such as wet chemical, dry, andphotoresist removal; thermal oxidation of silicon; electroplating andelectroless plating; diffusion processes, such as boron, phosphorus,arsenic, and antimony diffusion; ion implantation; film deposition, suchas evaporation (filament, electron beam, flash, and shadowing and stepcoverage), sputtering, chemical vapor deposition (CVD), plasma enhancedCVD, epitaxy (vapor phase, liquid phase, and molecular beam),electroplating, screen printing, and lamination. See generally Jaeger,Introduction to Microelectronic Fabrication (Addison-Wesley PublishingCo., Reading Mass. 1988); Runyan, et al., Semiconductor IntegratedCircuit Processing Technology (Addison-Wesley Publishing Co., ReadingMass. 1990); Proceedings of the IEEE Micro Electro Mechanical SystemsConference 1987-1998; Rai-Choudhury, ed., Handbook of Microlithography,Micromachining & Microfabrication (SPIE Optical Engineering Press,Bellingham, Wash. 1997).

More specifically, multiple layers of material (typically alternatingbetween metals and dielectrics) are deposited on top of a substrateforming a stack. After one or more layers of material are added to thestack, patterns are applied to a top most layer of the stack markingmaterial either to be removed from, or to remain on, the stack. Variousetching techniques, including wet or dry etches or reactive ion etching,are then applied to the patterned stack to remove unwanted material. Theetch process may remove material from one or more layers of the stackbased on the chemistry of the etch, the layers in the stack, and theamount of time the etch is applied. The manufacturing process mayinclude multiple iterations of layering, patterning, and etching.

In one implementation the shutter assemblies 102 are fabricated upon atransparent glass or plastic substrate. This substrate may be made anintegral part of a backlight which acts to evenly distribute theillumination from lamp 105 before the light exits through apertures 114.Alternatively and optionally the transparent substrate may be placed ontop of a planar light guide, wherein the array of shutter assemblies 102act as light modulation elements in the formation of an image. In oneimplementation the shutter assemblies 102 are fabricated in conjunctionwith or subsequent to the fabrication of a thin film transistor (TFT)array on the same glass or plastic substrate. The TFT array provides aswitching matrix for distribution of electrical signals to the shutterassemblies.

The process also includes a release step. To provide freedom for partsto move in the resulting device, sacrificial material is interdisposedin the stack proximate to material that will form moving parts in thecompleted device. An etch removes much of the sacrificial material,thereby freeing the parts to move.

After release, one or more of the surfaces of the shutter assembly maybe insulated so that charge does not transfer between moving parts uponcontact. This can be accomplished by thermal oxidation and/or byconformal chemical vapor deposition of an insulator such as Al2O3,Cr2O3, TiO2, TiSiO4, HfO2, HfSiO4, V2O5, Nb2O5, Ta2O5, SiO2, or Si3N4 orby depositing similar materials using techniques such as atomic layerdeposition and others. The insulated surfaces are chemically passivatedto prevent problems such as stiction between surfaces in contact bychemical conversion processes such as fluoridation, silanization, orhydrogenation of the insulated surfaces.

Dual compliant electrode actuators make up one suitable class ofactuators for driving the shutters 112 in the shutter assemblies 102. Adual compliant beam electrode actuator, in general, is formed from twoor more at least partially compliant beams. At least two of the beamsserve as electrodes (also referred to herein as “beam electrodes”). Inresponse to applying a voltage across the beam electrodes, the beamselectrodes are attracted to one another from the resultant electrostaticforces. Both beams in a dual compliant beam electrode are, at least inpart, compliant. That is, at least some portion of each of the beams canflex and or bend to aid in the beams being brought together. In someimplementations the compliance is achieved by the inclusion of flexuresor pin joints. Some portion of the beams may be substantially rigid orfixed in place. Preferably, at least the majority of the length of thebeams are compliant.

Dual compliant electrode actuators have advantages over other actuatorsknown in the art. Electrostatic comb drives are well suited foractuating over relatively long distances, but can generate onlyrelatively weak forces. Parallel plate or parallel beam actuators cangenerate relatively large forces but require small gaps between theparallel plates or beams and therefore only actuate over relativelysmall distances. R. Legtenberg et. al. (Journal ofMicroelectromechanical Systems v.6, p. 257, 1997) demonstrated how theuse of curved electrode actuators can generate relatively large forcesand result in relatively large displacements. The voltages required toinitiate actuation in Legtenberg, however, are still substantial. Asshown herein such voltages can be reduced by allowing for the movementor flexure of both electrodes.

In a dual compliant beam electrode actuator-based shutter assembly, ashutter is coupled to at least one beam of a dual compliant beamelectrode actuator. As one of the beams in the actuator is pulledtowards the other, the pulled beam moves the shutter, too. In doing so,the shutter is moved from a first position to a second position. In oneof the positions, the shutter interacts with light in an optical pathby, for example, and without limitation, blocking, reflecting,absorbing, filtering, polarizing, diffracting, or otherwise altering aproperty or path of the light. The shutter may be coated with areflective or light absorbing film to improve its interferentialproperties. In the second position, the shutter allows the light to passby, relatively unobstructed.

FIGS. 2A and 2B are diagrams of two embodiments of cantilever dualcompliant beam electrode actuator based-shutter assemblies for use in adisplay apparatus, such as display apparatus 100. More particularly,FIG. 2A depicts a cantilever dual compliant beam electrodeactuator-based shutter assembly 200 a (“shutter assembly 200 a”). Theshutter assembly 200 a modulates light to form an image by controllablymoving a shutter 202 a in and out of an optical path of light. In oneembodiment, the optical path begins behind a surface 204 a, to which theshutter 202 a is attached. The surface 204 a is illustrated as dashedboundary line. The dashed line indicates that the surface 204 a extendsbeyond the space delimited by the boundary line. Similar dashed boundarylines are used in other figures to indicate the same. The light passesthrough an aperture 206 a in the surface 204 a towards a viewer ortowards a display screen. In another embodiment, the optical path beginsin front of the surface 204 a and is reflected back to the viewer fromthe surface of the aperture 206 a.

The shutter 202 a of the shutter assembly 200 a is formed from a solid,substantially planar, body. The shutter 202 a can take virtually anyshape, either regular or irregular, such that in a closed position theshutter 202 a sufficiently obstructs the optical path through theaperture 206 a in the surface 204 a. In addition, the shutter 202 a musthave a width consistent with the width of the aperture, that, in theopen position (as depicted), sufficient light can pass through theaperture 206 a in the surface 204 a to illuminate a pixel, or contributeto the illumination of a pixel, in the display apparatus.

The shutter 202 a couples to one end of a load beam 208 a. A load anchor210 a, at the opposite end of the load beam 208 a physically connectsthe load beam 208 a to the surface 204 a and electrically connects theload beam 208 a to driver circuitry in the surface 204 a. Together, theload 208 a beam and load anchor 210 a serve as a mechanical support forsupporting the shutter 202 a over the surface 204 a.

The shutter assembly 200 a includes a pair of drive beams 212 a and 214a, one located along either side of the load beam 210 a. Together, thedrive beams 212 a and 214 a and the load beam 210 a form an actuator.One drive beam 212 a serves as a shutter open electrode and the otherdrive beam 214 a serves as a shutter close electrode. Drive anchors 216a and 218 a located at the ends of the drive beams 212 a and 214 aclosest to the shutter 202 a physically and electrically connects eachdrive beam 212 a and 214 a to the surface 204 a. In this embodiment, theother ends and most of the lengths of the drive beams 212 a and 214 aremain unanchored or free. The free ends of the drive beams 212 a and214 a are closer to the anchored end of the load beam 208 a than theanchored ends of the drive beams 212 a and 214 a are to shutter end ofthe load beam 208 a.

The load beam 208 a and the drive beams 212 a and 214 a are compliant.That is, they have sufficient flexibility and resiliency that they canbe bent out of their unstressed (“rest”) position or shape to at leastsome useful degree, without fatigue or fracture. As the load beam 208 aand the drive beams 212 a and 214 a are anchored only at one end, themajority of the lengths of the beams 208 a, 212 a, and 214 a is free tomove, bend, flex, or deform in response to an applied force. Theoperation of the cantilever dual compliant beam electrode actuatorbased-shutter assembly 200 a is discussed further below in relation toFIG. 3.

FIG. 2B is a second illustrative embodiment of a cantilever dualcompliant beam electrode actuator-based shutter assembly 200 b (shutterassembly 200 b). Like the shutter assembly 200 a, the shutter assembly200 b includes a shutter 202 b, coupled to a load beam 208 b, and twodrive beams 212 b and 214 b. The shutter 202 b is positioned in betweenits fully open position and its fully closed position. The load beam 208b and the drive beams 212 b and 214 b, together, form an actuator. Driveanchors 210 b, 216 b and 218 b, coupled to each end of the beams connectthe beams to a surface 204 b. In contrast to the shutter assembly 200 a,the shutter of shutter assembly 200 b includes several shutter apertures220, in the form of slots. The surface 204 b, instead of only having oneaperture, includes one surface aperture 206 b corresponding to eachshutter aperture 220. In the open position, the shutter apertures 220substantially align with the apertures 206 b in the surface 204 b,allowing light to pass through the shutter 202 b. In the closedposition, the surface apertures 206 b are obstructed by the remainder ofthe shutter 202 b, thereby preventing the passage of light.

Changing the state of a shutter assembly that includes multiple shutterapertures with a corresponding number of surface apertures requires lessshutter movement than changing the state of a shutter assemblyincorporating a solid shutter and single surface aperture, while stillproviding for the same aperture area. Reduced required motioncorresponds to lower required actuation voltage. More particularly, adecrease in required motion by ⅓ reduces the necessary actuation voltageof the actuator by a factor of about ⅓. Reduced actuation voltagefurther corresponds to reduced power consumption. Since the totalaperture area for either shutter assembly is about the same, eachshutter assembly provides a substantially similar brightness.

In other implementations, the shutter apertures and correspondingsurface apertures have shapes other than slots. The apertures may becircular, polygonal or irregular. In alternative implementations, theshutter may include more shutter apertures than there are surfaceapertures in the shutter assembly. In such implementations, one or moreof the shutter apertures may be serve as a filter, such as color filter.For example, the shutter assembly may have three shutter apertures forevery surface aperture, each shutter aperture including a red, blue, orgreen colored filter.

FIGS. 3A and 3B are diagrams illustrating the relationship between the,displacement at the end of the load beam and the relative voltage neededto move the load beam closer to the drive beam. The displacement thatcan be achieved at any given voltage depends, at least in part, on thecurvature or shape of the drive beam, or more precisely, on how theseparation, d, and the bending stress along the drive beam and the loadbeam varies as a function of position x along the load beam A separationfunction d(x), shown in FIG. 3A can be generalized to the form ofd=ax^(n), where y is the distance between the beams. For example, ifn=1, the distance between drive electrode and load electrode increaselinearly along the length of the load electrode. If n=2, the distanceincreases parabolically. In general, assuming a constant voltage, as thedistance between the compliant electrodes decreases, the electrostaticforce at any point on the beams increases proportional to 1/d. At thesame time, however, any deformation of the load beam which mightdecrease the separation distance may also results in a higher stressstate in the beam. Below a minimum threshold voltage a limit ofdeformation will be reached at which any electrical energy released by acloser approach of the electrodes is exactly balanced by the energywhich becomes stored in the deformation energy of the beams.

As indicated in the diagram 3B, for actuators having separationfunctions in which n is less than or equal to 2, the application of aminimum actuation voltage (V₂) results in a cascading attraction of theload beam to the drive beam without requiring the application of ahigher voltage. For such actuators, the incremental increase inelectrostatic force on the beams resulting from the load beam gettingcloser to the drive beam is greater than the incremental increase instress on the beams needed for further displacement of the beams.

For actuators having separation functions in which x is greater than 2,the application of a particular voltage results in a distinct partialdisplacement of the load electrode. That is, the incremental increase inelectrostatic force on the beams resulting from a particular decrease inseparation between the beams, at some point, fails to exceed theincremental deformation force needed to be imparted on the load beam tocontinue reducing the separation. Thus, for actuators having separationfunctions having n greater than 2, the application of a first voltagelevel results in a first corresponding displacement of the loadelectrode. A higher voltage results in a greater correspondingdisplacement of the load electrode. How the shapes and relativecompliance of thin beam electrodes effects actuation voltage isdiscussed in more detail in the following references: (R. Legtenberg et.al., Journal of Microelectromechanical Systems v.6, p. 257 (1997) and J.Li et. al. Transducers '03, The 12^(th) International Conference onSolid State Sensors, Actuators, and Microsystems, p. 480 (2003) each ofwhich is incorporated herein by reference

Referring back to FIGS. 2A and 2B, a display apparatus incorporating theshutter assemblies 202 a and 202 b actuates, i.e., changes the positionof the shutter assemblies 202 a and 202 b, by applying an electricpotential, from a controllable voltage source, to one of the drive beams212 a, 212 b, 214 a, or 214 b via its corresponding drive anchor 216 a,216 b, 218 a, or 218 b, with the load beam 208 a or 208 b beingelectrically coupled to ground, resulting in a voltage across the beams208 a, 208 b, 212 a, 212 b, 214 a, 214 b. The controllable voltagesource, such as an active matrix array driver, is electrically coupledto load beam 208 a or 208 b via an active matrix array (see FIGS. 9 and10 below). The display apparatus may instead apply an potential to theload beam 208 a or 208 b via the load anchor 210 a or 210 b of theshutter assembly 202 a or 202 b to increase the voltage. An electricalpotential difference between the drive beams and the load beams,regardless of sign or ground potential, will generate an electrostaticforce between the beams.

With reference back to FIG. 3, the shutter assembly 200 a of FIG. 2A hasa second order separation function (i.e., n=2). Thus, if the voltage orpotential difference between the beams 208 a and 212 a or 214 a of theshutter assembly 202 a at their point of least separation exceeds theminimum actuation voltage (V₂) the deformation of the beams 208 a and212 a or 214 a cascades down the entire lengths of the beams 208 a and212 a or 214 a, pulling the shutter end of the load beam 208 a towardsthe anchored end of the drive beam 212 a or 214 a. The motion of theload beam 208 a displaces the shutter 202 a such that it changes itsposition from either open to closed, or visa versa, depending on towhich drive beam 212 a or 214 a the display apparatus applied thepotential. To reverse the position change, the display apparatus ceasesapplication of the potential to the energized drive beam 212 a or 214 a.Upon the display apparatus ceasing to apply the potential, energy storedin the form of stress on the deformed load beam 208 a restores the loadbeam 208 a to its original or rest position. To increase the speed ofthe restoration and to reduce any oscillation about the rest position ofthe load beam 208 a, the display apparatus may return the shutter 202 ato its prior position by applying an electric potential to the opposingdrive beam 212 a or 214 a.

This shutter assemblies 200 a and 200 b, as well as shutter assemblies500 (see FIG. 5 below), 600 (see FIG. 6 below), 700 (see FIG. 7 below)and 800 (see FIG. 8 below) have the property of being electricallybi-stable. Generally, this is understood to encompass, although not belimited to, devices wherein the electrical potential V₂ that initiatesmovement between open and closed states is generally greater than theelectrical potential (V₁) required to keep the shutter assembly in astable state. Once the load beam 208 a and one of the drive beams are incontact, a substantially greater electrical force is to be applied fromthe opposing drive beam to move or separate the load beam, suchelectrical force being greater than would be necessary if the load beam208 a were to begin in a neutral or non-contact position. The bistabledevices described herein may employ a passive matrix driving scheme forthe operation of an array of shutter assemblies such as 200 a. In apassive matrix driving sequence it is possible to preserve an image bymaintaining a stabilization voltage V₁ across all shutter assemblies(except those that are being actively driven to a state change). With noor substantially no electrical power required, maintenance of apotential V₁ between the load beam 208 a and drive beam 212 a or 214 ais sufficient to maintain the shutter assembly in either its open orclosed states. In order to effect a switching event the voltage betweenload beam 208 a and the previously affected drive beam (for instance 212a) is allowed to return from V₁ to zero while the voltage between theload beam 208 a and the opposing beam (for instance 212 b) is brought upto the switching voltage V₂.

In FIG. 2B, the actuator has a third order separation function (i.e.,n=3). Thus applying a particular potential to one of the drive beams 212b or 214 b results in an incremental displacement of the shutter 202 b.The display apparatus takes advantage of the ability to incrementallydisplace the shutter 202 b to generate a grayscale image. For example,the application of a first potential to a drive beam 212 or 214 bdisplaces the shutter 202 b to its illustrated position, partiallyobstructing light passing through the surface apertures 206 b, but stillallowing some light to pass through the shutter 202 b. The applicationof other potentials results in other shutter 202 b positions, includingfully open, fully closed, and other intermediate positions between fullyopen and fully closed. In such fashion electrically analog drivecircuitry may be employed in order to achieve an analog grayscale image.

FIGS. 3C through 3F demonstrate the stages of motion of the load beam208 a, the shutter close electrode 214 a, and the shutter 202 a of theshutter assembly 200 a of FIG. 2A. The initial separation between thecompliant beams 208 a and 214 a fits a second order separation function.FIG. 3C shows the load beam 208 a in a neutral position with no voltageapplied. The aperture 206 a is half-covered by the shutter 212 a.

FIG. 3D demonstrates the initial steps of actuation. A small voltage isapplied between the load beam 208 a and the shutter close electrode 214a. The free end of the shutter close electrode 214 a has moved to makecontact with the load beam 208 a.

FIG. 3E shows the shutter assembly 200 a at a point of actuation afterthe shutter 212 begins to move towards the shutter close electrode 214a.

FIG. 3F shows the end state of actuation of the shutter assembly 200 a.The voltage has exceeded the threshold for actuation. The shutterassembly 200 a is in the closed position. Contact is made between theload beam 208 a and the shutter closed electrode 214 a all along itslength.

FIG. 4A is first cross sectional diagram of dual compliant electrodemirror-based light modulator 400 for inclusion in a display apparatus,such as display apparatus 100, instead of, or in addition to, theshutter assemblies 102. The mirror-based-based light modulator 400includes a mechanically compliant reflection platform 402. At least aportion of the reflection platform 402 is itself reflective or is coatedwith or is connected to a reflective material.

The reflection platform 402 may or may not be conductive. Inimplementations in which the reflection platform 402 is conductive, thereflection platform serves as a load electrode for the mirror-basedlight modulator 400. The reflection platform 402 is physically supportedover, and is electrically coupled to, a substrate 404 via a compliantsupport member 406. If the reflection platform 402 is formed from anon-conductive material, the reflection platform 402 is coupled to acompliant conductive load beam or other form of compliant loadelectrode. A compliant support member 406 physically supports thecombined reflection platform 402 and electrode over the substrate 404.The support member 406 also provides an electrical connection from theelectrode to the substrate 404.

The mirror-based light modulator 400 includes a second compliantelectrode 408, which serves a drive electrode 408. The drive electrode408 is supported between the substrate 404 and the reflection platform402 by a substantially rigid second support member 410. The secondsupport member 410 also electrically connects the second compliantelectrode 408 to a voltage source for driving the mirror-based lightmodulator 400.

The mirror-based light modulator 400 depicted in FIG. 4A is in restposition in which neither of the electrodes 402 or 408 carry apotential. FIG. 4B depicts the mirror-based light modulator 400 in anactivated state. When a potential difference is generated between thedrive electrode 408 and the load electrode 402 (be it the reflectiveplatform 402 or an attached load beam), the load electrode 402 is drawntowards the drive electrode 408, thereby bending the compliant supportbeam 406 and angling the reflective portion of the reflection platform402 to be least partially transverse to the substrate 404.

To form an image, light 412 is directed at an array of mirror-basedlight modulators 400 at a particular angle. Mirror-based lightmodulators 400 in their rest states reflect the light 412 away from theviewer or the display screen, and mirror-based light modulators in theactive state reflect the light 412 towards a viewer or a display screen,or visa versa.

FIG. 5 is a diagram of another cantilever dual compliant beam electrodeactuator-based shutter assembly 500 (“shutter assembly 500”). As withthe shutter assemblies 200 a and 200 b, the shutter assembly 500includes a shutter 502 coupled to a compliant load beam 504. Thecompliant load beam 504 is then physically anchored to a surface 506,and electrically coupled to ground, at its opposite end via a loadanchor 508. The shutter assembly 500 includes only one compliant drivebeam 510, located substantially alongside the load beam 504. The drivebeam 510, in response to being energized with an electric potential froma controllable voltage source draws the shutter 502 from a firstposition (in which the load beam 504 is substantially unstressed) in aplane substantially parallel to the surface, to a second position inwhich the load beam 504 is stressed. When the potential is removed, thestored stress in the load beam 504 restores the load beam 504 to itsoriginal position.

In addition, in comparison to the shutter assemblies 202 a and 202 b,the load beam 504 has a width which varies along its length. The loadbeam 504 is wider near its anchor 508 than it is nearer to the shutter502. In comparison to the shutter assemblies 202 a and 202 b and becauseof its tailored width, the load beam 504 typically has an overallgreater stiffness. Shutter assemblies incorporating stiffer beamstypically require higher voltages for actuation, but in return, allowfor higher switching rates. For example, the shutter assemblies 202 aand 202 b may be switched up to about 10 kHz, while the stiffer shutterassembly 500 may be switched up to about 100 kHz.

FIG. 6 is diagram of a shutter assembly 600 incorporating two dualcompliant electrode beam actuators 602 (“actuators 602”), according toan illustrative embodiment of the invention. The shutter assembly 600includes a shutter 604. The shutter 604 may be solid, or it may includeone or more shutter apertures as described in relation to FIG. 2B. Theshutter 604 couples on one side to the beam actuators 602. Together, theactuators 602 move the shutter transversely over a surface in plane ofmotion which is substantially parallel to the surface.

Each actuator 602 includes a compliant load member 606 connecting theshutter 604 to a load anchor 608. The compliant load members 606 eachinclude a load beam 610 and an L bracket 612. The load anchors 608 alongwith the compliant load members 606 serve as mechanical supports,keeping the shutter 604 suspended proximate to the surface. The loadanchors 608 physically connect the compliant load members 606 and theshutter 604 to the surface and electrically connect the load beams 610of the load members 606 to ground. The coupling of the shutter 604 fromtwo positions on one side of the shutter 604 to load anchors 608 inpositions on either side of the shutter assembly 600 help reducetwisting motion of the shutter 604 about its central axis 614 duringmotion.

The L brackets 612 reduce the in-plane stiffness of the load beam. 610.That is, the L brackets 612 reduce the resistance of actuators 602 tomovement in a plane parallel to the surface (referred to as “in-planemovement” 615), by relieving axial stresses in the load beam.

Each actuator 602 also includes a compliant drive beam 616 positionedadjacent to each load beam 610. The drive beams 616 couple at one end toa drive beam anchor 618 shared between the drive beams 616. The otherend of each drive beam 616 is free to move. Each drive beam 616 iscurved such that it is closest to the load beam 610 near the free end ofthe drive beam 616 and the anchored end of the load beam 610.

In operation, a display apparatus incorporating the shutter assembly 600applies an electric potential to the drive beams 616 via the drive beamanchor 618. As a result of a potential difference between the drivebeams 616 and the load beam 610, the free ends of the drive beams 616are pulled towards the anchored ends of the load beams 610 and theshutter ends of the load beams 610 are pulled toward the anchored endsof the drive beams 616. The electrostatic force draws the shutter 604towards the drive anchor 618. The compliant members 606 act as springs,such that when the electrical potentials are removed from the drivebeams 616, the load beams compliant members 606 push the shutter 604back into its initial position, releasing the stress stored in the loadbeams 610. The L brackets 612 also serve as springs, applying furtherrestoration force to the shutter 604.

In fabrication of shutter assemblies 200 through 800, as well as forshutter assemblies 1300 through 1800 it is preferable to provide arectangular shape for the cross section of the load beams (such as loadbeams 610) and the drive beams (such as drive beams 616). By providing abeam thickness (in the direction perpendicular to surface) which is 1.4times or more larger in dimension than the beam width (in a directionparallel to the surface) the stiffness of the load beam 610 will beincreased for out-of-plane motion 617 versus in-plane motion 615. Such adimensional and, by consequence, stiffness differential helps to ensurethat the motion of the shutter 604, initiated by the actuators 602, isrestricted to motion along the surface and across the surface aperturesas opposed to out-of-plane motion 617 which would a wasteful applicationof energy. It is preferable for certain applications that the crosssection of the load beams (such as 610) be rectangular as opposed tocurved or elliptical in shape. The strongest actuation force is achievedif the opposing beam electrodes have flat faces so that upon actuationthey can approach and touch each other with the smallest possibleseparation distance.

FIG. 7 is a diagram of a second shutter assembly 700 incorporating twodual compliant electrode beam actuators 702, according to anillustrative embodiment of the invention. The shutter assembly 700 takesthe same general form of the shutter assembly 600, other than itincludes a return spring 704. As with the shutter assembly 600, in theshutter assembly 700, two actuators 702 couple to a first side of ashutter 706 to translate the shutter 706 in a plane parallel to asurface over which the shutter is physically supported. The returnspring 704 couples to the opposite side of the shutter 706. The returnspring 704 also couples to the surface at a spring anchor 708, acting asan additional mechanical support. By physically supporting the shutter706 over the surface at opposite sides of the shutter 706, the actuators702 and the return spring 704 reduce motion of the shutter 706 out ofthe plane of intended motion during operation. In addition, the returnspring 704 incorporates several bends which reduce the in-planestiffness of the return spring 704, thereby further promoting in-planemotion over out-of-plane motion. The return spring 704 provides anadditional restoration force to the shutter 706, such that once anactuation potential is removed, the shutter 706 returns to its initialposition quicker. The addition of the return spring 704 increases onlyslightly the potential needed to initiate actuation of the actuators702.

FIG. 8 is a diagram of a shutter assembly including a pair of shutteropen actuators 802 and 804 and a pair of shutter close actuators 806 and808, according to an illustrative embodiment of the invention. Each ofthe four actuators 802, 804, 806, and 808 take the form of a dualcompliant beam electrode actuator. Each actuator 802, 804, 806, and 808includes a compliant load member 810 coupling a shutter 812, at one end,to a load anchor 814, at the other end. Each compliant load member 810includes a load beam 816 and an L bracket 818. Each actuator 802, 804,806, and 808 also includes and a drive beam 820 with one end coupled toa drive anchor 822. Each pair of actuators 802/804 and 806/808 share acommon drive anchor 822. The unanchored end of each drive beam 820 ispositioned proximate to the anchored end of a corresponding compliantload member 810. The anchored end of each drive beam 820 is locatedproximate to the L bracket end of a corresponding load beam 816. In adeactivated state, the distance between a load beam 816 and itscorresponding drive beam 820 increases progressively from the anchoredend of the load beam 816 to the L bracket 818.

In operation, to open the shutter 812, a display apparatus incorporatingthe shutter assembly 800 applies an electric potential to the driveanchor 822 of the shutter open actuators 802 and 804, drawing theshutter 812 towards the open position. To close the shutter 812, thedisplay apparatus applies an electric potential to the drive anchor 822of the shutter close actuators 806 and 808 drawing the shutter 812towards the closed position. If neither pair of actuators 802/804 or806/808 are activated, the shutter 812 remains in an intermediateposition, somewhere between fully open and fully closed.

The shutter open actuators 802/804 and shutter closed actuators 806/808couple to the shutter 812 at opposite ends of the shutter. The shutteropen and closed actuators have their own load members 810, thus reducingthe actuation voltage of each actuator 802, 804, 806 and 808. Because ofthe electrical bi-stability described in reference to FIG. 3, it isadvantageous to find an actuation method or structure with er moreleverage for separating the compliant load member 810 from a drive beam820 with which it might be in contact. By positioning the open andclosed actuators 802/804 and 806/808 on opposite sides of the shutter812, the actuation force of the actuator-to-be-actuated is transferredto the actuator-to-be-separated through the shutter. The actuation forceis therefore applied to the task of separation at a point close to theshutter (for instance near the L-bracket end of the load beam 816) whereits leverage will be higher.

For shutter assemblies such as in FIG. 8 typical shutter widths (alongthe direction of the slots) will be in the range of 20 to 800 microns.The “throw distance” or distance over which the shutter will movebetween open and closed positions will be in the range of 4 to 100microns. The width of the drive beams and load beams will be in therange of 0.2 to 40 microns. The length of the drive beams and load beamswill be in the range of 10 to 600 microns. Such shutter assemblies maybe employed for displays with resolutions in the range of 30 to 1000dots per inch.

Each of the shutter assemblies 200 a, 200 b, 500, 600, 700 and 800, andthe mirror-based light modulator 400, described above fall into a classof light modulators referred to herein as “elastic light modulators.”Elastic light modulators have one mechanically stable rest state. In therest state, the light modulator may be on (open or reflecting), off(closed or not reflecting), or somewhere in between (partially open orpartially reflecting). If the generation of a voltage across beams in anactuator forces the light modulator out of its rest state into amechanically unstable state, some level of voltage across the beams mustbe maintained for the light modulator to remain in that unstable state.

FIG. 9 is a diagram of an active matrix array 900 for controllingelastic light modulators 902 in a display apparatus. In particular, theactive matrix array 900 is suitable for controlling elastic lightmodulators 902, such as the mirror-based light modulator 400 orshutter-based light modulators 500, 600, and 700, that include only apassive restoration force. That is, these light modulators 902 requireelectrical activation of actuators to enter a mechanically unstablestate, but then utilize mechanical mechanisms, such as springs, toreturn to the rest state.

The active matrix array is fabricated as a diffused orthin-film-deposited electrical circuit on the surface of a substrate onwhich the elastic light modulators 902 are formed. The active matrixarray 900 includes a series of row electrodes 904 and column electrodes906 forming a grid like pattern on the substrate, dividing the substrateinto a plurality of grid segments 908. The active matrix array 900includes a set of drivers 910 and an array of non-linear electricalcomponents, comprised of either diodes or transistors that selectivelyapply potentials to grid segments 908 to control one or more elasticlight modulators 902 contained within the grid segments 908. The art ofthin film transistor arrays is described in Active Matrix Liquid CrystalDisplays: Fundamentals and Applications by Willem den Boer (Elsevier,Amsterdam, 2005).

Each grid segment 908 contributes to the illumination of a pixel, andincludes one or more elastic light modulators 902. In grid segmentsincluding only a single elastic light modulator 902, the grid segment908 includes, in addition to the elastic light modulator 902, least onediode or transistor 912 and optionally a capacitor 914. The capacitor914 shown in FIG. 9 can be explicitly added as a design element of thecircuit, or it can be understood that the capacitor 914 represents theequivalent parallel or parasitic capacitance of the elastic lightmodulator. The emitter 916 of the transistor 912 is electricallycoupled, to either the drive electrode or the load electrode of theelastic light modulator 902. The other electrode of the actuator iscoupled to a ground or common potential. The base 918 of the transistor912 electrically couples to a row electrode 904 controlling a row ofgrid segments. When the base 918 of the transistor receives a potentialvia the row electrode 904, current can run through the transistor 912from a corresponding column electrode 906 to generate a potential in thecapacitor 914 and to apply a potential to the drive electrode of theelastic light modulator 902 activating the actuator.

The active matrix array 900 generates an image, in one implementationby, one at a time, applying a potential from one of the drivers 910 to aselected row electrode 904, activating a corresponding row of gridsegments 908. While a particular row is activated, the display apparatusapplies a potential to the column electrodes corresponding to gridsegments in the active row containing light modulators which need to beswitched out of a rest state.

When a row is subsequently deactivated, a stored charge will remain onthe electrodes of the actuator 902 (as determined by the equivalentcapacitance of the actuator) as well as, optionally, on the parallelcapacitor 914 that can be designed into the circuit., keeping theelastic shutter mechanisms 902 in their mechanically unstable states.The elastic shutter mechanism 902 remains in the mechanically unstablestate until the voltage stored in the capacitor 914 dissipates or untilthe voltage is intentionally reset to ground potential during asubsequent row selection or activation step.

FIG. 10 is diagram of another implementation of an active matrix array1000 for controlling elastic light modulators 1002 in a displayapparatus. In particular, the active matrix array 1000 is suitable forcontrolling elastic light modulators, such as shutter-based lightmodulators 200 a, 200 b, and 800, which include one set of actuators forforcing the light modulators from a rest state to a mechanicallyunstable state and a second set of actuators for driving the lightmodulators back to the rest state and possibly to a second mechanicallyunstable state. Active matrix array 1000 can also be used for drivingnon-elastic light modulators described further in relation to FIGS.12-20.

The active matrix array 1000 includes one row electrode 1004 for eachrow in the active matrix array 1000 and two column electrodes 1006 a and1006 b for each column in the active matrix array 1000. For example, fordisplay apparatus including shutter-based light modulators, one columnelectrode 1006 a for each column corresponds to the shutter openactuators of light modulators 1002 in the column. The other columnelectrode 1006 b corresponds to the shutter close actuators of the lightmodulators 1002 in the column. The active matrix array 1000 divides thesubstrate upon which it is deposited into grid sections 1008. Each gridsection 1008 includes one or more light modulators 1002 and at least twodiodes or transistors 1010 a and 1010 b and optionally two capacitors1012 a and 1012 b. The bases 1014 a and 1014 b of each transistor 1010 aand 1010 b are electrically coupled to a column electrode 1006 a or 1006b. The emitters 1016 a and 1016 b of the transistors 1010 a and 1010 bare coupled to a corresponding capacitor 1012 a or 1012 b and a driveelectrode of the light modulator(s) 1002 in the grid section 1008.

In operation, a driver applies a potential to a selected row electrode1004, activating the row. The active matrix array 1000 selectivelyapplies potentials to one of the two column electrodes 1006 a or 1006 bof each column in which the state of the light modulator(s) 1002 in thegrid section 1008 needs to be changed. Alternatively, the active matrixarray 1000 may also apply a potential to column electrodes 1006 a or1006 b for grid sections 1008 previously in an active state which are toremain in an active state.

For both active matrix arrays 900 and 1000, the drivers powering thecolumn electrodes, in some implementations, select from multiplepossible potentials to apply to individual column electrodes 1006 a and1006 b. The light modulator(s) 1002 in those columns can then be openedor closed different amounts to create grayscale images.

FIG. 11 is a cross sectional view of the shutter-assembly 800 of FIG. 8along the line labeled A-A′. Referring to FIGS. 8, 10, and 11, theshutter assembly 800 is built on substrate 1102 which is shared withother shutter assemblies of a display apparatus, such as displayapparatus 100, incorporating the shutter assembly 800. The voltagesignals to actuate the shutter assembly, are transmitted alongconductors in underlying layers of the shutter assembly. is The voltagesignals are controlled by an active matrix array, such as active matrixarray 1000. The substrate 1102 may support as many as 4,000,000 shutterassemblies, arranged in up to about 2000 rows and up to about 2000columns.

In addition to the shutter 812, the shutter open actuators 802 and 804,the shutter close actuators 806 and 808, the load anchors 814 and thedrive anchors 822, the shutter assembly 800 includes a row electrode1104, a shutter open electrode 1106, a shutter close electrode 1108, andthree surface apertures 1110. The depicted shutter assembly has at leastthree functional layers, which may be referred to as the row conductorlayer, the column conductor layer, and the shutter layer. The shutterassembly is preferably made on a transparent substrate such as glass orplastic. Alternatively the substrate can be made from an opaque materialsuch as silicon, as long as through holes are provided at the positionsof each of the surface apertures 1110 for the transmission of light. Thefirst metal layer on top of the substrate is the row conductor layerwhich is patterned into row conductor electrodes 1104 as well asreflective surface sections 1105. The reflective surface sections 1105reflect light passing through the substrate 1102 back through thesubstrate 1102 except at the surface apertures 1110. In someimplementations the surface apertures may include or be covered by red,green, or blue color filtering materials.

The shutter open electrode 1106 and the shutter close electrode 1108 areformed in a column conductor layer 1112 deposited on the substrate 1102,on top of the row conductor layer 1104. The column conductor layer 1112is separated from the row conductor layer 1104 by one or moreintervening layers of dielectric material or metal. The shutter openelectrode 1104 and the shutter close electrode 1106 of the shutterassembly 800 are shared with other shutter assemblies in the same columnof the display apparatus. The column conductor layer 1112 also serves toreflect light passing through gaps in the ground electrode 1104 otherthan through the surface apertures 1110. The row conductor layer 1104and the column conductor layer 1112 are between about 0.1 and about 2microns thick. In alternative implementations, the column conductor 1112layer can be located below the row conductor layer 1104. In anotheralternative implementation both the column conductor layer and the rowconductor layer may be located above the shutter layer.

The shutter 812, the shutter open actuators 802 and 804, the shutterclose actuators 806 and 808, the load anchors 814 and the drive anchors822 are formed from third functional layer of the shutter assembly 800,referred to as the shutter layer 1114. The actuators 802, 804, 806, and808 are formed from a deposited metal, such as, without limitation, Au,Cr or Ni, or a deposited semiconductor, such as, without limitation aspolycrystalline silicon, or amorphous silicon, or from single crystalsilicon if formed on top of a buried oxide (also known as silicon oninsulator). The beams of the actuators 802, 804, 806, and 808 arepatterned to dimensions of about 0.2 to about 20 microns in width. Theshutter thickness is typically in the range of 0.5 microns to 10microns. To promote the in-plane movement of the shutters (i.e. reducethe transverse beam stiffness as opposed to the out-of-plane stiffness),it is preferable to maintain a beam dimensional ratio of about at least1.4:1, with the beams being thicker than they are wide.

Metal or semiconductor vias electrically connect the row electrode 1104and the shutter open electrode 1106 and the shutter close electrode 1108of the column conductor layer 1112 to features on the shutter layer1114. Specifically, vias 1116 electrically couple the row electrode 1104to the load anchors 814 of the shutter assembly 800, keeping thecompliant load member 810 of the shutter open actuators 802 and 804 andthe shutter close actuators 806 and 808, as well as the shutter 812, atthe row conductor potential. Additional vias electrically couple theshutter open electrode 1106 to the drive beams 820 of the shutter openactuators 802 and 804 via the drive anchor 822 shared by the shutteropen actuators 802 and 804. Still other vias electrically couple theshutter close electrode 1108 to the drive beams 820 of the of theshutter close actuators 806 and 808 via the drive anchor 822 shared bythe shutter close actuators 806 and 808.

The shutter layer 1114 is separated from the column conductor layer 1112by a lubricant, vacuum or air, providing the shutter 812 freedom ofmovement. The moving pieces in the shutter layer 1114 are mechanicallyseparated from neighboring components (except their anchor points 814)in a release step, which can be a chemical etch or ashing process, whichremoves a sacrificial material from between all moving parts.

The diodes, transistors, and/or capacitors (not shown for purpose ofclarity) employed in the active matrix array may be patterned into theexisting structure of the three functional layers, or they can be builtinto separate layers that are disposed either between the shutterassembly and the substrate or on top of the shutter layer. Thereflective surface sections 1105 may be patterned as extensions of therow and column conductor electrodes or they can be patterned asfree-standing or electrically floating sections of reflective material.Alternatively the reflective surface sections 1105 along with theirassociated surface apertures 1110 can be patterned into a fourthfunctional layer, disposed between the shutter assembly and thesubstrate, and formed from either a deposited metal layer or adielectric mirror. Grounding conductors may be added separately from therow conductor electrodes in layer 1104. These separate groundingconductors may be required when the rows are activated throughtransistors, such as is the case with an active matrix array. Thegrounding conductors can be either laid out in parallel with the rowelectrodes (and bussed together in the drive circuits), or the groundingelectrodes can be placed into separate layers between the shutterassembly and the substrate.

In addition to elastic light modulators, display apparatus can includebi-stable light modulators, for example bi-stable shutter assemblies. Asdescribed above, a shutter in an elastic shutter assembly has onemechanically stable position (the “rest position”), with all othershutter positions being mechanically unstable. The shutter of abi-stable shutter assembly, on the other hand, has two mechanicallystable positions, for example, open and closed. Mechanically bi-stableshutter assemblies have the advantage that no voltage is required tomaintain the shutters in either the open or the closed positions.Bi-stable shutter assemblies can be further subdivided into two classes:shutter assemblies in which each stable position is substantiallyenergetically equal, and shutter assemblies in which one stable positionis energetically preferential to the other mechanically stable position.

FIG. 12 is a diagram 1200 of potential energy stored in three types ofshutter assemblies in relation to shutter position. The solid line 1202corresponds to an elastic shutter assembly. The dashed line 1204corresponds to a bi-stable shutter assembly with equal energy stablestates. The dotted line 1206 corresponds to a bi-stable shutter assemblywith non-equal energy stable states. As indicated in the energy diagram1200, the energy curves 1204 and 1206 for the two types of bi-stableshutter assemblies each include two local minima 1208, corresponding tostable shutter positions, such as fully open 1210 and fully closed 1212.As illustrated, energy must be added to the a assembly in order to moveits shutters out of the positions corresponding to one of the localminima. For the bi-stable shutter assemblies with non-equal-energymechanically stable shutter positions, however, the work needed to opena shutter 1212 is greater than the work required to close the shutter1214. For the elastic shutter assembly, on the other hand, opening theshutter requires work 1218, but the shutter closes spontaneously afterremoval of the control voltage.

FIG. 13A is a top view of a shutter layer 1300 of a bi-stable shutterassembly. The shutter layer 1360 includes a shutter 1302 driven by twodual compliant electrode actuators 1304 and 1306. The shutter 1302includes three slotted shutter apertures 1308. One dual compliantelectrode actuator 1304 serves as a shutter open actuator. The otherdual compliant electrode actuator 1306 serves as a shutter closeactuator.

Each dual compliant electrode actuator 1304 and 1306 includes acompliant member 1310 connecting the shutter 1302, at about its linearaxis 1312, to two load anchors 1314, located in the corners of theshutter layer 1300. The compliant members 1310 each include a conductiveload beam 1316, which may have an insulator disposed on part of, or theentirety of its surface. The load beams 1316 server as mechanicalsupports, physically supporting the shutter 1302 over a substrate onwhich the shutter assembly is built. The actuators 1304 and 1306 alsoeach include two compliant drive beams 1318 extending from a shareddrive anchor 1320. Each drive anchor 1320 physically and electricallyconnects the drive beams 1318 to the substrate. The drive beams 1318 ofthe actuators 1304 and 1306 curve away from their corresponding driveanchors 1320 towards the points on the load anchors 1314 at which loadbeams 1316 couple to the load anchors 1314. These curves in the drivebeams 1318 act to reduce the stiffness of the drive beams, therebyhelping to decrease the actuation voltage.

Each load beam 1316 is generally curved, for example in a bowed (orsinusoidal) shape. The extent of the bow is determined by the relativedistance between the load anchors 1314 and the length of the load beam1316. The curvatures of the load beams 1316 provide the bi-stability forthe shutter assembly 1300. As the load beam 1316 is compliant, the loadbeam 1316 can either bow towards or away from the drive anchor 1320. Thedirection of the bow changes depending on what position the shutter 1302is in. As depicted, the shutter 1302 is in the closed position. The loadbeam 1316 of the shutter open actuator 1304 bows away from the driveanchor 1320 of the shutter open actuator 1304. The load beam 1316 of theshutter closed actuator 1306 bows towards the drive anchor 1320 of theshutter close actuator 1306.

In operation, to change states, for example from closed to open, adisplay apparatus applies a potential to the drive beams 1318 of theshutter open actuator 1304. The display apparatus may also apply anpotential to the load beams 1316 of the shutter open actuator. Anyelectrical potential difference between the drive beams and the loadbeams, regardless of sign with respect to a ground potential, willgenerate an electrostatic force between the beams. The resultant voltagebetween the drive beams 1318 and the load beams 1316 of the shutter openactuator 1304 results in an electrostatic force, drawing the beams 1316and 1318 together. If the voltage is sufficiently strong, the load beam1316 deforms until its curvature is substantially reversed, as depictedin the shutter close actuator in FIG. 13A.

FIG. 13B shows the evolution of force versus displacement for thegeneral case of bi-stable actuation, including that for FIG. 13A.Referring to FIGS. 13A and 13B, generally the force required to deform acompliant load beam will increase with the amount of displacement.However, in the case of a bi-stable mechanism, such as illustrated inFIG. 13A, a point is reached (point B in FIG. 13B) where further travelleads to a decrease in force. With sufficient voltage applied betweenthe load beam 1316 and the drive beam 1318 of the shutter open actuator1304, a deformation corresponding to point B of FIG. 13B is reached,where further application of force leads to a large and spontaneousdeformation (a “snaphthrough”) and the deformation comes to rest atpoint C in FIG. 13B. Upon removal of a voltage, the mechanism will relaxto a point of stability, or zero force. Point D is such a relaxation orstable point representing the open position. To move the shutter 1302 inthe opposite direction it is first necessary to apply a voltage betweenthe load beam 1316 and the drive beam 1318 of the shutter close actuator1306. Again a point is reached where further forcing results in a largeand spontaneous deformation (point E). Further forcing in the closeddirection results in a deformation represented by point F. Upon removalof the voltage, the mechanism relaxes to its initial and stable closedposition, point A.

In FIG. 13A, the length of the compliant member is longer than thestraight-line distance between the anchor and the attachment point atthe shutter. Constrained by the anchor points, the load beam finds astable shape by adapting a curved shape, two of which shapes constituteconfigurations of local minima in the potential energy. Otherconfigurations of the load beam involve deformations with additionalstrain energy.

For load beams fabricated in silicon, typical as-designed widths areabout 0.2 μm to about 10 μm. Typical as-designed lengths are about 20 μmto about 1000 μm. Typical as-designed beam thicknesses are about 0.2 μmto about 10 μm. The amount by which the load beam is pre-bent istypically greater than three times the as-designed width

The load beams of FIG. 13A can be designed such that one of the twocurved positions is close to a global minimum, i.e. possesses the lowestenergy or relaxed state, typically a state close to zero energy storedas a deformation or stress in the beam. Such a design configuration maybe referred to as “pre-bent”, meaning, among other things, that theshape of the compliant member is patterned into the mask such thatlittle or no deformation is required after release of the shutterassembly from the substrate. The as-designed and curved shape of thecompliant member is close to its stable or relaxed state. Such a relaxedstate holds for one of the two shutter positions, either the open or theclosed position. When switching the shutter assembly into the otherstable state (which can be referred to as a metastable state) somestrain energy will have to be stored in the deformation of the beam; thetwo states will therefore have unequal potential energies; and lesselectrical energy will be required to move the beam from metastable tostable states as compared to the motion from the stable state to themetastable state.

Another design configuration for FIG. 13A, however, can be described asa pre-stressed design. The pre-stressed design provides for two stablestates with equivalent potential energies. This can be achieved forinstance by patterning the compliant member such that upon release ofthe shutter assembly will substantially and spontaneously deform intoits stable shape (i.e. the initial state is designed to be unstable).Preferably the two stable shapes are similar such that the deformationor strain energy stored in the compliant member of each of those stablestates will be similar. The work required to move between open andclosed shutter positions for a pre-stressed design will be similar.

The pre-stress condition of the shutter assembly can be provided by anumber of means. The condition can be imposed post-manufacture by, forinstance, mechanically packaging the substrate to induce a substratecurvature and thus a surface strain in the system. A pre-stressedcondition can also be imposed as a thin film stress imposed by surfacelayers on or around the load beams. These thin film stresses result fromthe particulars of a deposition processes. Deposition parameters thatcan impart a thin film stress include thin film material composition,deposition rate, and ion bombardment rate during the deposition process.

In FIG. 13A, the load beam is curved in each of its locally stablestates and the load beam is also curved at all points of deformation inbetween the stable states. The compliant member may be comprised,however, of any number of straight or rigid sections of load beam aswill be described in the following figures. In FIG. 18, furthermore,will be shown the design of a bi-stable shutter assembly in whichneither of the two equivalent stable positions possesses, requires, oraccumulates any significant deformation or strain energy. Stress isstored in the system temporarily as it is moved between the stablestates.

FIG. 14 is an top view of the shutter layer 1400 of a second bi-stableshutter assembly. As described above in relation to FIG. 6, reducingresistance to in-plane motion tends to reduce out-of-plane movement ofthe shutter. The shutter layer 1400 is similar to that of the shutterlayer 1300, other than the shutter layer 1400 includes an in-planestiffness-reducing feature, which promotes in-plane movement, and adeformation promoter which promotes proper transition between states. Aswith the shutter layer 1300 of FIG. 13A, the shutter layer 1400 of FIG.14 includes load beams 1402 coupling load anchors 1404 to a shutter1406. To reduce the in-plane stiffness of the shutter assembly and toprovide some axial compliance to the load beams 1402, the load anchors1404 couple to the load beams 1402 via springs 1408. The springs 1408can be formed from flexures, L brackets, or curved portions of the loadbeams 1402.

In addition, the widths of the load beams 1402 vary along their lengths.In particular, the beams are narrower along sections where they meet theload anchors 1404 and the shutter 1406. The points along the load beams1402 at which the load beams 1402 become wider serve as pivot points1410 to confine deformation of the load beams 1402 to the narrowersections 1410.]

FIG. 15 is a top view of a shutter layer 1500 of a tri-stable shutterassembly incorporating dual compliant electrode actuators, according toan illustrative embodiment of the invention. The shutter layer 1500includes a shutter open actuator 1502 and a shutter close actuator 1504.Each actuator 1502 and 1504 includes two compliant drive beams 1506physically and electrically coupled to a substrate of a displayapparatus by a drive anchor 1508.

The shutter open actuator 1502, by itself, is an elastic actuator,having one mechanically stable state. Unless otherwise constrained, theshutter open actuator 1502, after actuation would return to its reststate. The shutter open actuator 1502 includes two load beams 1510coupled to load anchors 1512 by L brackets 1514 at one end and to theshutter 1516 via L brackets 1518 at the other end. In the rest state ofthe shutter open actuator 1502, the load beams 1510 are straight. The Lbrackets 1514 and 1518 allow the load beams 1510 to deform towards thedrive beams 1506 of the shutter open actuator 1502 upon actuation of theshutter open actuator 1502 and away form the drive beams 1506 uponactuation of the shutter close actuator 1504.

The shutter close actuator 1504 is similarly inherently elastic. Theshutter close actuator 1504 includes a single load beam 1520 coupled toa load anchor 1522 at one end. When not under stress, i.e., in its reststate, the load beam 1520 is straight. At the opposite end of the loadbeam 1520 of the shutter close actuator 1504, the load beam 1520 iscoupled to a stabilizer 1524 formed from two curved compliant beams 1526connected at their ends and at the center of their lengths. The beams1526 of the stabilizer 1524 have two mechanically stable positions:bowed away from the shutter close actuator 1504 (as depicted) and bowedtowards the shutter close actuator 1504.

In operation, if either the shutter open actuator 1502 or the shutterclose actuator are activated 1504, the load beam 1520 of the shutterclose actuator 1504 is deformed to bow towards the shutter open actuator1504 or towards the drive beams 1528 of the shutter close actuator 1504,respectively, as the shutter 1516 is moved into an actuated position. Ineither case, the length of the shutter close actuator 1504 load beam1520 with respect to the width of the shutter layer 1500 as a whole, isreduced, pulling the beams 1526 of the stabilizer 1524 to bow towardsthe shutter close actuator 1504. After the activated actuator isdeactivated, the energy needed to deform the beams 1526 of thestabilizer 1524 back to its original position is greater than the energystored in the load beams 1510 and 1520 and of the actuators 1502 and1504. Additional energy must be added to the system to return theshutter 1516 to its rest position. Thus, the shutter 1516 in the shutterassembly has three mechanically stable positions, open, half open, andclosed.

FIGS. 16A-C are diagrams of another embodiment of a bi-stable shutterassembly 1600, illustrating the state of the shutter assembly 1600during a change in shutter 1602 position. The shutter assembly 1600includes a shutter 1602 physically supported by a pair of compliantsupport beams 1604. The support beams couple to anchors 1603 as well asto the shutter 1602 by means of rotary joints 1605. These joints may beunderstood to consist of pin joints, flexures or thin connector beams.In the absence of stress being applied to the support beams 1604, thesupport beams 1604 are substantially straight.

FIG. 16A depicts the shutter 1602 in an open position, FIG. 16B depictsthe shutter 1602 in the midst of a transition to the closed position,and FIG. 16C shows the shutter 1602 in a closed position. The shutterassembly 1600 relies upon an electrostatic comb drive for actuation. Thecomb drive is comprised of a rigid open electrode 1608 and a rigidclosed electrode 1610. The shutter 1602 also adopts a comb shape whichis complementary to the shape of the open and closed electrodes. Combdrives such as are shown in FIG. 16 are capable of actuating overreasonably long translational distances, but at a cost of a reducedactuation force. The primary electrical fields between electrodes in acomb drive are aligned generally perpendicular to the direction oftravel, therefore the force of actuation is generally not along thelines of the greatest electrical pressure experienced by the interiorsurfaces of the comb drive.

Unlike the bi-stable shutter assemblies described above, instead ofrelying upon a particular curvature of one or more beams to providemechanical stability, the bi-stable actuator 1600 relies on the straightrelaxed state of its support beams 1604 to provide mechanical stability.For example, in its two mechanically stable positions, depicted in FIGS.16A and 16C, the compliant support beams 1604 are substantially straightat an angle to the linear axis 1606 of the shutter assembly 1600. Asdepicted in FIG. 16B, in which the shutter 1602 is in transition fromone mechanically stable position to the other, the support beams 1604physically deform or buckle to accommodate the movement. The forceneeded to change the position of the shutter 1602 must therefore besufficient to overcome the resultant stress on the compliant supportbeams 1604. Any energy difference between the open and closed states ofshutter assembly 1600 is represented by a small amount of elastic energyin the rotary joints 1605.

The shutter 1602 is coupled to two positions on either side of theshutter 1602 through support beams 1604 to anchors 1603 in positions oneither side of the shutter assembly 1600, thereby reducing any twistingor rotational motion of the shutter 1602 about its central axis. The useof compliant support beams 1604 connected to separate anchors onopposite sides of the shutter 1602 also constrains the movement of theshutter along a linear translational axis. In another implementation, apair of substantially parallel compliant support beams 1604 can becoupled to each side of shutter 1602. Each of the four support beamscouples at independent and opposing points on the shutter 1602. Thisparallelogram approach to support of the shutter 1602 helps to guaranteethat linear translational motion of the shutter is possible.

FIG. 17A depicts a bi-stable shutter assembly 1700, in which the beams1702 incorporated into the shutter assembly 1700 are substantially rigidas opposed to compliant, in both of the shutter assembly's stablepositions 17A-1 and 17A-3 as well as in a transitional position 17A-2.The shutter assembly 1700 includes a shutter 1704 driven by a pair ofdual compliant beam electrode actuators 1706. Two compliant members 1710support the shutter 1704 over a surface 1712. The compliant members 1710couple to opposite sides of the shutter 1704. The other ends of thecompliant members 1710 couple to anchors 1714, connecting the compliantmembers 1710 to the surface 1712. Each compliant member 1710 includestwo substantially rigid beams 1716 coupled to a flexure or othercompliant element 1718, such as a spring or cantilever arm. Even thoughthe beams 1716 in the compliant members are rigid, the incorporation ofthe compliant element 1718 allows the compliant member 1710 as a wholeto change its shape in a compliant fashion to take on two mechanicallystable shapes. The compliant element is allowed to relax to its reststate in either of the closed or open positions of the shutter assembly(see 17A-1 and 17A-3), so that both of the end states possesssubstantially identical potential energies. No permanent beam bending orbeam stressing is required to establish the stability of the two endstates, although strain energy is stored in the compliant element 1718during the transition between states (see 17A-2).

The shape of the compliant element 1718 is such that a relatively easyin-plane translation of the shutter 1704 is allowed while out-of-planemotion of the shutter is restricted.

The actuation of the bi-stable shutter assembly 1700 is accomplished bya pair of elastic dual compliant beam electrode actuators 1706, similarto the actuators employed in FIG. 15. In shutter assembly 1700 theactuators 1706 are physically separated and distinct from the compliantmembers 1710. The compliant members 1710 provide a relatively rigidsupport for the shutter 1704 while providing the bi-stability requiredto sustain the open and closed states. The actuators 1706 provide thedriving force necessary to switch the shutter between the open andclosed states.

Each actuator 1706 comprises a compliant load member 1720. One end ofthe compliant load member 1720 is coupled to the shutter 1704, while theother end is free. In shutter assembly 1700 the compliant load membersin actuators 1706 a are not coupled to anchors or otherwise connected tothe surface 1712. The drive beams 1722 of the actuators 1706 are coupledto anchors 1724 and thereby connected to the surface 1712. In thisfashion the voltage of actuation is reduced.

FIG. 17B is a diagram of a bi-stable shutter assembly 1700 b in whichthe shutter 1702 b is designed to rotate upon actuation. The shutter1702 b is supported at four points along its periphery by 4 compliantsupport beams 1704 b which are coupled to four anchors 1706 b. As inFIG. 16, the compliant support beams 1704 b are substantially straightin their rest state. Upon rotation of the shutter 1702 b the compliantmembers will deform as the distance between the anchors and the shutterperiphery decreases. There are two low energy stable states in which thecompliant support beams 1704 b are substantially straight. The shuttermechanism in 1700 b has the advantage that there is no center of massmotion in the shutter 1702 b.

The shutter 1702 b in shutter assembly 1700 b has a plurality of shutterapertures 1708 b, each of possesses a segmented shape designed to makemaximum use of the rotational motion of the shutter. FIG. 18 is adiagram of a bi-stable shutter assembly 1800 incorporatingthermoelectric actuators 1802 and 1804. The shutter assembly 1800includes a shutter 1806 with a set of slotted shutter apertures 1808.Thermoelectric actuators 1802 and 1804 couple to either side of theshutter 1806 for moving the shutter 1806 transversely in a planesubstantially parallel to a surface 1808 over which the shutter 1806 issupported. The coupling of the shutter 1806 from two positions on eitherside of the shutter 1806 to load anchors 1807 in positions on eitherside of the shutter assembly 1800 help reduce any twisting or rotationalmotion of the shutter 1806 about its central axis.

Each thermoelectric actuator 1802 and 1804 includes three compliantbeams 1810, 1812, and 1814. Compliant beams 1810 and 1812 are eachthinner than compliant beam 1814. Each of the beams 1810, 1812, and 1814is curved in an s-like shape, holding the shutter 1806 stably inposition.

In operation, to change the position of the shutter from open (asdepicted) to closed, current is passed through a circuit including beams1810 and 1814. The thinner beams 1810 in each actuator 1802 and 1804heat, and therefore also expands, faster than the thicker beam 1814. Theexpansion forces the beams 1810, 1812, and 1814 from their mechanicallystable curvature, resulting in transverse motion of the shutter 1806 tothe closed position. To open the shutter 1806, current is run through acircuit including beams 1812 and 1814, resulting in a similardisproportionate heating and expansion of beams 1812, resulting in theshutter 1806 being forced back to the open position.

Bi-stable shutter assemblies can be driven using a passive matrix arrayor an active matrix array. FIG. 19 is a diagram of a passive matrixarray 1900 for controlling bi-stable shutter assemblies 1902 to generatean image. As with active matrix arrays, such as active matrix arrays 900and 1000, the passive matrix array 1900 is fabricated as a diffused orthin-film-deposited electrical circuit on a substrate 1904 of a displayapparatus. In general, passive matrix arrays 1900 require less circuitryto implement than active matrix arrays 900 and 1000, and are easier tofabricate. The passive matrix array 1900 divides the shutter assemblies1902 on the substrate 1904 of the display apparatus into rows andcolumns of grid segments 1906 of a grid. Each grid segment 1906 mayinclude one or more bi-stable shutter assemblies 1902. In the displayapparatus, all grid segments 1906 in a given row of the gird share asingle row electrode 1908. Each row electrode 1908 electrically couplesa controllable voltage source, such as driver 1910 to the load anchorsof the shutter assemblies 1902. All shutter assemblies 1902 in a columnshare two common column electrodes, a shutter open electrode 1912 and ashutter close electrode 1914. The shutter open electrode 1912 for agiven column electrically couples a driver 1910 to the drive electrodeof the shutter open actuator of the shutter assemblies 1902 in thecolumn. The shutter close electrode 1914 for a given column electricallycouples a driver 1910 to the drive electrode of the shutter closeactuator of the shutter assemblies 1902 in the column.

The shutter assemblies 1300, 1400, 1500, 1600, 1700 a, and 1800 areamenable to the use of a passive matrix array because their property ofmechanical bi-stability makes it possible to switch between open andclosed states if the voltage across the actuator exceeds a minimumthreshold voltage. If the drivers 1910 are programmed such that none ofthem will output a voltage that by itself is sufficient to switch theshutter assemblies between open and closed states, then a given shutterassembly will be switched if its actuator receives voltages from twoopposing drivers 1910. The shutter assembly at the intersection of aparticular row and column can be switched if it receives voltages fromits particular row and column drivers whose difference exceeds theminimum threshold voltage.

To change the state of a shutter assembly 1902 from a closed state to anopen state, i.e., to open the shutter assembly 1902, a driver 1910applies a potential to the row electrode 1908 corresponding to the rowof the grid in which the shutter assembly 1902 is located. A seconddriver 1910 applies a second potential, in some cases having an oppositepolarity, to the shutter open electrode 1912 corresponding to the columnin the grid in which the shutter assembly 1902 is located. To change thestate of a shutter assembly 1902 from an open state to a closed state,i.e., to close the shutter assembly 1902, a driver 1910 applies apotential to the row electrode 1908 corresponding to the row of thedisplay apparatus in which the shutter assembly 1902 is located. Asecond driver 1910 applies a second potential, in some cases having anopposite polarity, to the shutter close electrode 1914 corresponding tothe column in the display apparatus in which the shutter assembly 1902is located. In one implementation, a shutter assembly 1902 changes statein response to the difference in potential applied to the row electrode1908 and one of the column electrodes 1912 or 1914 exceeding apredetermined switching threshold.

To form an image, in one implementation, a display apparatus sets thestate of the shutter assemblies 1902 in the grid, one row at a time insequential order. For a given row, the display apparatus first closeseach shutter assembly 1902 in the row by applying a potential to thecorresponding row electrodes 1908 and a pulse of potential to all of theshutter close electrodes 1914. Then, the display apparatus opens theshutter assemblies 1902 through which light is to pass by applying apotential to the shutter open electrode 1912 and applying a potential tothe row electrodes 1908 for the rows which include shutter assemblies1902 in the row which are to be opened. In one alternative mode ofoperation, instead of closing each row of shutter assemblies 1902sequentially, after all rows in the display apparatus are set to theproper position to form an image, the display apparatus globally resetsall shutter assemblies 1902 at the same time by applying a potentials toall shutter close electrodes 1914 and all row electrodes 1908concurrently. In another alternative mode of operation, the displayapparatus forgoes resetting the shutter assemblies 1902 and only altersthe states of shutter assemblies 1902 that need to change state todisplay a subsequent image. A number of alternate driver control schemesfor images have been proposed for use with ferroelectric liquid crystaldisplays, many of which can be incorporated for use with themechanically bi-stable displays herein. These technologies are describedin Liquid Crystal Displays: Driving Schemes and Electro-Optical Effects,Ernst Lieder (Wiley, New York, 2001).

The physical layout of the display is often a compromise between thecharacteristics of resolution, aperture area, and driving voltage. Smallpixel sizes are generally sought to increase the resolution of thedisplay. As pixels become smaller, however, proportionally the roomavailable for shutter apertures decreases. Designers seek to maximizeaperture ratio as this increases the brightness and power efficiency ofthe display. Additionally, the combination of a small pixels and largeaperture ratios implies large angular deformations in the compliantmembers that support the shutters, which tends to increase the drivevoltages required and the energy dissipated by the switching circuitry.

FIGS. 20A and 20B demonstrate two methods of tiling shutter assembliesinto an array of pixels to maximize the aperture ratios in dense arraysand minimize the drive voltages.

FIG. 20A, for example, depicts a tiling 2000 of two cantilever dual beamelectrode actuator-based shutter assemblies 2002 and 2004 tiled to forma rhombehedral pixel 2006 from two generally triangular shutterassemblies 2002 and 2004. The shutter assemblies 2002 and 2004 may beindependently or collectively controlled. The rhombehedral tiling ofFIG. 20A is quite close to a rectangular tiling arrangement, and in factadapted to a rectangular pixel with aspect ratio of 2:1. Since twoshutter assemblies can be established within each rectangle, such a 2:1rectangular tiling arrangement can further be attached or built on topof an active matrix array which possesses a square repeating distancebetween rows and columns. A 1 to 1 correlation between pixels in the twoarrays can therefore be established. Square pixel arrays are mostcommonly employed for the display of text and graphic images. Theadvantage of the layout in FIG. 20B is that it is understood to maximizethe length of the load beams in each triangular pixel to reduce thevoltage required for switching shutters between open and closed states.

FIG. 20B is an illustrative tiling of a plurality of bi-stable dualcompliant beam electrode-actuator-based shutter assemblies 1300 of FIG.13A. In comparison, for example, to the bi-stable dual compliant beamelectrode-actuator-based shutter assembly 1400 of FIG. 14, the width ofthe shutter 1302 of the shutter assembly 1300 is substantially less thanthe distance between the load anchors 1314 of the shutter assembly 1300.While the narrower shutter 1302 allows for less light to pass througheach shutter assembly 1300, the extra space can be utilized for tighterpacking of shutter assemblies 1300, as depicted in FIG. 20B, withoutloss of length in the load beams. The longer load beams makes itpossible to switch the shutters in the array at reduced voltages. Inparticular, the narrower shutter 1302 enables portions of the actuators1304 and 1306 of the shutter assemblies 1300 interleave with the gapsbetween actuators 1302 and 1304 of neighboring shutter assemblies 1300.The interleaved arrangement of FIG. 20B can nevertheless still be mappedonto a square arrangement of rows and columns, which is the common pixelconfiguration for textual displays.

The tiling or pixel arrangements for shutter assemblies need not belimited to the constraints of a square array. Dense tiling can also beachieved using rectangular, rhombehedral, or hexagonal arrays of pixels,all of which find applications, for example in video and color imagingdisplays.

FIG. 21 is a cross sectional view of a display apparatus 2100incorporating dual compliant electrode actuator-based shutter assemblies2102. The shutter assemblies 2102 are disposed on a glass substrate2104. A reflective film 2106 disposed on the substrate 2104 defines aplurality of surface apertures 2108 located beneath the closed positionsof the shutters 2110 of the shutter assemblies 2102. The reflective film2106 reflects light not passing through the surface apertures 2108 backtowards the rear of the display apparatus 2100. An optional diffuser2112 and an optional brightness enhancing film 2114 can separate thesubstrate 2104 from a backlight 2116. The backlight 2116 is illuminatedby one or more light sources 2118. The light sources 2118 can be, forexample, and without limitation, incandescent lamps, fluorescent lamps,lasers, or light emitting diodes. A reflective film 2120 is disposedbehind the backlight 2116, reflecting light towards the shutterassemblies 2102. Light rays from the backlight that do not pass throughone of the shutter assemblies 2102 will be returned to the backlight andreflected again from the film 2120. In this fashion light that fails toleave the display to form an image on the first pass can be recycled andmade available for transmission through other open apertures in thearray of shutter assemblies 2102. Such light recycling has been shown toincrease the illumination efficiency of the display. A cover plate 2122forms the front of the display apparatus 2100. The rear side of thecover plate 2122 can be covered with a black matrix 2124 to increasecontrast. The cover plate 2122 is supported a predetermined distanceaway from the shutter assemblies 2102 forming a gap 2126. The gap 2126is maintained by mechanical supports and/or by an epoxy seal 2128attaching the cover plate 2122 to the substrate 2104. The epoxy 2128should have a curing temperature preferably below about 200 C. it shouldhave a coefficient of thermal expansion preferably below about 50 ppmper degree C. and should be moisture resistant. An exemplary epoxy 2128is EPO-TEK B9021-1, sold by Epoxy Technology, Inc.

The epoxy seal 2128 seals in a working fluid 2130. The working fluid2130 is engineered with viscosities preferably below about 10 centipoiseand with relative dielectric constant preferably above about 2.0, anddielectric breakdown strengths above about 10⁴ V/cm. The working fluid2130 can also serve as a lubricant. Its mechanical and electricalproperties are also effective at reducing the voltage necessary formoving the shutter between open and closed positions. In oneimplementation, the working fluid 2130 preferably has a low refractiveindex, preferably less than about 1.5. In another implementation theworking fluid 2130 has a refractive index that matches that of thesubstrate 2104. Suitable working fluids 2130 include, withoutlimitation, de-ionized water, methanol, ethanol, silicone oils,fluorinated silicone oils, dimethylsiloxane, polydimethylsiloxane,hexamethyldisiloxane, and diethylbenzene.

A sheet metal or molded plastic assembly bracket 2132 holds the coverplate 2122, shutter assemblies 2102, the substrate 2104, the backlight2116 and the other component parts together around the edges. Theassembly bracket 2132 is fastened with screws or indent tabs to addrigidity to the combined display apparatus 2100. In someimplementations, the light source 2118 is molded in place by an epoxypotting compound.

1. A display apparatus comprising: a shutter for interacting with alight in an optical path to form an image on the display apparatus; avoltage input for receiving an actuation potential; and an actuator,responsive to an actuation potential being applied to the voltage input,for moving the shutter from a first mechanically stable position in aplane to a second mechanically stable position in the plane.
 2. Thedisplay apparatus of claim 1, wherein the actuator comprises a spring.3. The display apparatus of claim 1, wherein the stiffness of the firstcompliant member varies along its length.
 4. The display apparatus ofclaim 1, wherein the shutter comprises a plurality of shutter aperturesthrough which light can pass.
 5. The display apparatus of claim 1,wherein the actuator, responsive to a second actuation potential beingapplied to the voltage input, moves the shutter from one of the firstand second mechanically stable states to a third mechanically stablestate.
 6. The display apparatus of claim 1, comprising a passive matrixarray for selectively applying the actuation potential to the voltageinput to form the image.
 7. The display apparatus of claim 1, whereinthe first compliant member includes a plurality of non-compliant memberscoupled by a plurality of compliant joints.
 8. The display apparatus ofclaim 1, comprising a stabilizer having first and second mechanicallystable states, wherein the movement of the shutter switches the state ofthe stabilizer between the first and second mechanically stable states.9. The display apparatus of claim 1, wherein the first compliant memberis shaped such that the work required to move the shutter from the firstmechanically stable position to the second mechanically stable positionis substantially equal to the work required to move the shutter from thesecond mechanically stable position to the first mechanically stableposition.
 10. The display apparatus of claim 1, wherein the firstcompliant member is shaped such that the work required to move theshutter from the first mechanically stable position to the secondmechanically stable position is greater than the work required to movethe shutter from the second mechanically stable position to the firstmechanically stable position.
 11. The display apparatus of claim 1,comprising a second actuator coupled to the shutter, wherein the secondactuator has first and second mechanically stable states correspondingto the first and second mechanically stable positions of the shutter.12. The display apparatus of claim 11, wherein the actuator couples tothe shutter in a first location and the second actuator couples to theshutter in a second location.
 13. The display apparatus of claim 11,wherein the actuator couples to a first side of the shutter and thesecond actuator couples to a second side of the shutter substantiallyopposite the first side.
 14. The display apparatus of claim 1,comprising a first compliant member having a first mechanically stablestate corresponding to the first mechanically stable position of themodulator and a second mechanically stable state corresponding to thesecond mechanically stable position of the modulator.
 15. The displayapparatus of claim 14, wherein the first compliant member comprises afirst beam, and wherein in the first mechanically stable state, thefirst beam is bowed in a first direction, and in the second mechanicallystable state, the beam is bowed in a second direction.
 16. The displayapparatus of claim 14, wherein the first compliant member, absent theapplication of force to the compliant member has a substantiallystraight shape.
 17. The display apparatus of claim 14, wherein in boththe first mechanically stable state and the second mechanically stablestate, the first compliant member is substantially straight.
 18. Thedisplay apparatus of claim 14, wherein, responsive to the voltage inputreceiving the actuation potential, the first compliant member deformsfrom the first stable state to the second stable state.
 19. The displayapparatus of claim 14, wherein moving the actuator from either of thefirst and second mechanically stable states requires the actuator toapply force to the first compliant member.
 20. The display apparatus ofclaim 14, wherein the height of the compliant member is at least about1.4 times the width of the compliant member.
 21. The display apparatusof claim 14, wherein the compliant member is between about 0.5 μm andabout 5 μm wide.
 22. The display apparatus of claim 14, wherein thefirst compliant member comprises an insulator at least partiallycovering the first compliant member.
 23. The display apparatus of claim22, wherein the dielectric constant of the insulator is greater than orequal to about
 2. 24. The display apparatus of claim 14, wherein theactuator comprises a second compliant member having a second beam with acorresponding bow.
 25. The display apparatus of claim 24, wherein thefirst compliant member comprises a first beam having a correspondingbow, and, in the first mechanically stable state, the bow of the secondbeam is substantially the same as the bow of the first beam and in thesecond mechanically stable state, the bow of the second beam issubstantially opposite the bow of the first beam.
 26. The displayapparatus of claim 14, wherein the first compliant member couples to theshutter to a first anchor connecting the first compliant member to asurface over which the shutter is moved.
 27. The display apparatus ofclaim 26, wherein the first compliant member couples to a second anchorconnecting the first compliant member to the surface, and wherein thefirst anchor connects the first compliant member to a first location onthe surface and the second anchor connects the first compliant member toa second location on the surface.
 28. The display apparatus of claim 26,comprising a working fluid having a dielectric constant of at leastabout 1.5 disposed between the first and second compliant members. 29.The display apparatus of claim 14, comprising a second compliant memberhaving first and second mechanically stable states, and wherein in eachof the first and second mechanically stable states the second compliantmember is substantially straight.
 30. The display apparatus of claim 29,wherein the first compliant member couples to the shutter in a firstlocation on the shutter and the second compliant member couples to theshutter in a second location.
 31. The display apparatus of claim 29,wherein the second compliant member couples to an anchor connecting thesecond compliant member to a surface over which the shutter is moved.32. The display apparatus of claim 29, wherein the first and secondcompliant members are electrodes, which, in response to a voltage beingapplied across the first and second compliant members, are drawntogether, thereby moving the shutter.
 33. The display apparatus of claim14, comprising a second compliant member, wherein each of the first andsecond compliant members includes a beam, at least one which of has aflat side facing the other of the beam.
 34. The display apparatus ofclaim 1, wherein moving the shutter comprises rotation or translation ofthe shutter.
 35. A method of forming an image on a display apparatus,comprising: selectively applying an actuation potential to a voltageinput; moving a shutter, in response to the application of the actuationpotential, in a plane, from a first mechanically stable position to asecond mechanically stable position, thereby permitting light tocontribute to the formation of an image.
 36. The method of claim 35,wherein moving the shutter comprises deforming a compliant member towhich the shutter is coupled.
 37. The method of claim 35, wherein movingshutter comprises altering the curvature of a compliant member to whichthe shutter is coupled.
 38. The method of claim 35, comprising, inresponse to the application of the actuation potential, generating avoltage across two compliant members, drawing them together.